Neutrino Masses and the Gluino Axion Model
نویسندگان
چکیده
We extend the recently proposed gluino axion model to include neutrino masses. We discuss how the canonical seesaw model and the Higgs triplet model may be realized in this framework. In the former case, the heavy singlet neutrinos are contained in superfields which do not have any vacuum expectation value, whereas the gluino axion is contained in one which does. We also construct a specific renormalizable model which realizes the mass scale relationship MSUSY ∼ f2 a/MU , where fa is the axion decay constant and MU is a large effective mass parameter. A new axionic solution[1] to the strong CP problem was recently proposed[2]. Instead of coupling to ordinary matter as in the DFSZ model[3] or to unknown matter as in the KSVZ model[4], this new axion couples to the gluino as well as all other supersymmetric particles. The instanton-induced CP violating phase[5] of quantum chromodynamics is then canceled by the dynamical phase of the gluino mass, as opposed to that of the quarks in the DFSZ model and that of the unknown colored fermions in the KSVZ model. This means that CP violation is absent in the strong-interaction sector and experimental observables, such as the neutron electric dipole moment[6], are subject only to weak-interaction contributions. What sets the gluino axion model[2] apart from all other previous models is its identification of the Peccei-Quinn global symmetry U(1)PQ with the U(1)R symmetry of superfield transformations. Under U(1)R, the scalar components of a chiral superfield transform as φ → eφ, whereas the fermionic components transform as ψ → eiθ(R−1)ψ. In the Minimal Supersymmetric Standard Model (MSSM), the quark and lepton superfields Q̂, û, d̂, L̂, ê have R = +1 whereas the Higgs superfields Ĥu, Ĥd have R = 0. The superpotential Ŵ = μĤuĤd + huĤuQ̂û c + hdĤdQ̂d̂ c + heĤdL̂ê c (1) has R = +2 except for the μ term (which has R = 0). Hence the resulting Lagrangian breaks U(1)R explicitly, leaving only a discrete remnant, i.e. the usual R parity: R = (−1)3B+L+2J . The gluino axion model replaces μ with a singlet composite superfield of R = +2 so that the resulting supersymmetric Lagrangian is invariant under U(1)R. It also requires all supersymmetry breaking terms to be invariant under U(1)R, the spontaneous breaking of which then produces the axion and solves the strong CP problem. In the MSSM, neutrinos are massless. However, in view of the recent experimental evidence for neutrino oscillations, it is desirable to incorporate into any realistic model naturally small Majorana neutrino masses[7, 8]. In the following we will discuss how the canonical seesaw model[9] and the Higgs triplet model[10] may be realized in the framework 2 of the gluino axion model. In the case of the seesaw model, there are in fact proposals[11] that the axion scale is the same as that of the singlet neutrino masses. Consider first the Higgs triplet model. Add to the gluino axion model two triplet superfields: ξ̂1 = (ξ ++ 1 , ξ + 1 , ξ 0 1) : R = 0, (2) ξ̂2 = (ξ 0 2 , ξ − 2 , ξ −− 2 ) : R = +2, (3) then the superpotential (which is required to have R = +2) has the following additional terms: ∆Ŵ = mξ ξ̂1ξ̂2 + fij ξ̂1L̂iL̂j + hξ̂2ĤuĤu. (4) Note that the term ξ̂1ĤdĤd is forbidden. The resulting scalar potential has the term |mξξ1 + hHuHu|, hence the desired trilinear scalar interaction hmξξ 1HuHu +h.c. is there to combine with the Yukawa interaction fijξ1LiLj + h.c. to form the well-known dimension-5 effective operator[7] which generates the neutrino masses: (mν)ij = 2fijh 〈Hu〉 mξ . (5) If the intermediate scale mξ is assumed to be of order the U(1)R breaking scale, i.e. 10 11 GeV or so, then mν of order 1 eV is obtained if fijh is of order 10 −2. Consider next the canonical sesaw model. Add to the gluino axion model the singlet superfield N̂ with R = +1, then the superpotential is supplemented by ∆Ŵ = mNN̂N̂ + fiL̂iN̂Ĥu , (6) which generates the well-known seesaw neutrino mass (mν)ij = fifj 〈Hu〉 mN . (7)
منابع مشابه
Gluino Axion , Neutrino Seesaw , Dynamical Gaugino Mass , and A ≃ 0 Supersymmetry
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